Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q18 Paid Members Public
My Solution for "If $a \equiv b \pmod {n_{1}}$ and $a \equiv c \pmod {n2}$, prove that $b \equiv c \pmod {n}$, where the integer $n = gcd(n_{1}, n_{2})$."
Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q17 Paid Members Public
My Solution for "Prove that whenever $ab \equiv cd \pmod {n}$ and $b \equiv d \pmod {n}$, with $gcd(b, n) = 1$, then $a \equiv c \pmod {n}$."
Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q16 Paid Members Public
My Solution for "Use the theory of congruences to verify that $$89 \mid 2^{44} - 1 \qquad \text{and} \qquad 97 \mid 2 ^{48} - 1$$"
Techniques I learned from Playing Sekiro Paid Members Public
Struggling with Sekiro? Try the techniques I realized while playing Sekiro. From being stuck on Genichiro for four nights to mastering these techniques and defeating Isshin in just 3 hours.
Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q15 Paid Members Public
My Solution for "Establish that if $a$ is an odd integer, then for any $n \geq 1$$$a^{2^{n}} \equiv 1 \pmod {2^{n + 2}}$$ [Hint: Proceed by induction on $n$.]"
Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q14 Paid Members Public
My Solution for "Give an example to show that $a^{k} \equiv b^{k} \pmod {n}$ and $k \equiv j \pmod {n}$ need not imply that $a^{j} \equiv b^{j} \pmod {n}$."
Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q13 Paid Members Public
My Solution for "Verify that if $a \equiv b \pmod {n_{1}}$ and $a \equiv b \pmod {n_{2}}$, then $a \equiv b \pmod {n}$, where the integer $n = lcm(n_{1}, n_{2})$. Hence, whenever $n_{1}$ and $n_{2}$ are relatively prime, $a \equiv b \pmod{n_{1}n_{2}}$."
Elementary Number Theory Problems 4.2 Solution (David M. Burton's 7th Edition) - Q12 Paid Members Public
My Solution for "Prove the following statements: (a) If $gcd(a, n) = 1$, then the integers $$c, c + a, c + 2a, c + 3a, ... , c + (n - 1)a$$ form a complete set of residues modulo $n$ for any $c$. (b) Any $n$ consecutive integers form a complete set of residues modulo $n$. (c) The product of ..."
